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arXiv · 2003.04457

Gridless DOA Estimation and Root-MUSIC for Non-Uniform Arrays

Mark Wagner·Yongsung Park·Peter Gerstoft
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Abstract

The problem of gridless direction of arrival (DOA) estimation is addressed in the non-uniform array (NUA) case. Traditionally, gridless DOA estimation and root-MUSIC are only applicable for measurements from a uniform linear array (ULA). This is because the sample covariance matrix of ULA measurements has Toeplitz structure, and both algorithms are based on the Vandermonde decomposition of a Toeplitz matrix. The Vandermonde decomposition breaks a Toeplitz matrix into its harmonic components, from which the DOAs are estimated. First, we present the `irregular' Toeplitz matrix and irregular Vandermonde decomposition (IVD), which generalizes the Vandermonde decomposition to apply to a more general set of matrices. It is shown that the IVD is related to the MUSIC and root-MUSIC algorithms. Next, gridless DOA is generalized to the NUA case using IVD. The resulting non-convex optimization problem is solved using alternating projections (AP). A numerical analysis is performed on the AP based solution which shows that the generalization to NUAs has similar performance to traditional gridless DOA.

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Mark Wagner, Yongsung Park, Peter Gerstoft. 2020-03-09. Gridless DOA Estimation and Root-MUSIC for Non-Uniform Arrays. https://doi.org/10.1109/tsp.2021.3068353

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